Doing an Amazon book search for "website design" turns up a lot of promising results that are both inexpensive and highly-rated. The SitePoint books I've read are pragmatic and useful.

It's good that you know what you like when you see it. I'm no design expert, but I usually start by finding several Web sites that I really like, borrowing elements from each, and combining them into an original design. I don't mean stealing copyrighted content or images, but instead finding inspiration in what's already out there.

Being a good designer takes practice, and it helps to have some general artistic skill.

Design is much more than creating a beautiful interface. It should be functional, meaning that the user can get what they need, Easy to learn/use, and sufficiently attractive and professional enough to give users, especially new ones, confidence that what they can get from the site is worth having.

Once you have a much better idea of what the website needs to do and how it should work, it will be easier to dress it up a little with an appropriate design, since much of the underlying structural work has been done.

There are many excellent resources covering this, but my favorite is Boag World, the blog of Paul Boag. It covers all aspects of web design, including user experience, and does a very good job balancing all important aspects. They just stopped doing their weekly podcast, but the archives, which go back over 200 episodes, contain volumes of useful information.

Even if you are decent with the tools (Photoshop, Illustrator, whatever), it's still way too easy to end up with a lousy design. I've found that sharpening my wireframing skills has had one of the largest overall impacts to my design quality. As such, I highly recommend the following: